Vacuum fixture

ABSTRACT

Line voltage and line current signals are sensed on a power line having at least one conducting path. The sensed line voltages and line currents are converted into a digital signal. A phase-to-neutral voltage signal and phase current signal are computed from the digital signal to thereby define a phase of the power line. An interval of orthogonality is determined from the sensed voltage and current signals, coinciding with passage of an integral number of cycles of a fundamental frequency reference signal which is computed from the computed phase-to-neutral voltage signal. A vector metering quantity is computed for the determined interval of orthogonality from the computed phase-to-neutral voltage signal and the computed phase current signal. The vector metering quantities to be computed may be identified and computed based upon an associated detent. The vector metering quantity is also computed based on an identified circuit topology.

This is a divisional of co-pending application Ser. No. 08/564,543 filedon Nov. 30, 1995.

FIELD OF THE INVENTION

The present invention relates to electrical power line measurement, andmore particularly to apparatus and methods for metering vectorelectrical quantities for electrical power lines having multipleconducting paths.

BACKGROUND OF THE INVENTION

In the distribution of electrical energy, electric utility companieshave typically found it desirable to measure quantities related to thedelivery of electrical energy to a consumer which accurately reflect thecost of delivering that energy to that consumer, and thus equitablyapportion the cost of delivering energy among all the users of the powersystem. Early on, utilities realized that billing customers based merelyupon measurement of actual energy delivered--Watt-hours--fails toaccurately reflect the cost of delivering energy to the customer. Forexample, large industrial users may have inductive loads, such as largeinduction motors, which induce significant phase shifts between voltagesand currents in the power line, thus requiring advancement of generatorangles and capacitive compensation by the utility in order to maintainvoltage levels, efficiently deliver energy to consumers and preservestability in the power system. This added generation and capitalequipment cost is not reflected in measurements of energy delivered atthe customer metering point.

Accordingly, other measures of electric power have been developed. Forexample, utilities typically bill not only for real load energy aswatthours delivered to a user, but also reactive load quadergy asvarhours (or reactive volt-ampere hours), and power factor (cos θ). Bymeasuring both watthours and varhours eletric utilities can more aaccurately apportion the costs of supplying energy to those customerswith inductive loads which demand the most from the power deliverynetwork.

Potential errors in power measurement attributable to nonsinusoidalconditions were also recognized early in this century. Nearly sixtyyears ago, power systems engineers attempted to develop a generalunified theoretical model for power systems which accounts for harmonicsand distortion. This model is described in an article, "Definitions ofPower and Related Quantities" by Harvey L. Curtis and Francis B. Silsbeeof the National Bureau of Standards, published for the 1935 AIEE SummerConference. The definitions in the Curtis and Silsbee article arederived from a three-dimensional vector model of electrical powerapplicable for all harmonics and phases. These definitions have survivedlargely intact through the publication of the latest editions of the"IEEE Std 100, Standard Dictionary of Electrical and Electronic Terms."

Power vector relationships for a power line are illustrated in FIG. 19.The ANSI/IEEE STD 100 Dictionary of Electrical and Electronic Termsdefines "phasor power" S as the magnitude of a two-dimensional powervector whose rectangular components are "active power" P and "reactivepower" Q. In systems of more than one conducting path, i.e., "polyphase"systems and "single-phase" systems with more than one conducting path,phasor power S is the vector sum of active power P and reactive power Sfor the system, for all harmonics. As will be understood by thoseskilled in the art, phasor power S is equal to active power P when allload elements are resistive. In one form or another, it is phasor power,or more specifically phasor volt-ampere-hours, which utilities havetraditionally metered and billed. Typically, utilities have measuredphasor volt-ampere-hours for the fundamental frequency of the systemvoltage using conventional watthour meters and varhour meters.

"Apparent power" U is defined as the magnitude of a three-dimensionalvector power with orthogonal components of active power P, reactivepower Q and a third component, "distortion power" D. Apparent power andapparent volt-ampere-hours provide a more comprehensive measure of thecharacteristics of a power line. For an isolated two-terminal circuit,apparent power U may be treated as a scalar, the product of theroot-mean-square voltage and current in the single conducting path. In asystem having more than one conducting wire, however, vector apparentpower and vector apparent volt-ampere-hours are vectors, the vector sumof real, reactive and distortion power components for all phases andharmonics. For this reason, vector apparent power and vector apparentvolt-ampere-hours have been largely ignored as practical meteringquantities because of a lack of techniques to accurately measure theirvector components. Instead, utilities have relied on alternativemeasurements such as quadergy and phasor volt-ampere-hours, for whichmeasurement techniques and equipment could be easily developed.

Conventional sampling electronic watthour meters generally accuratelymeasure energy by accumulating instantaneous power measurements. This istypically achieved by sampling voltage and current on the power line andconverting the sampled voltages and currents into digital values whichmay be multiplied to compute the instantaneous power. These samplingproducts are accumulated to yield a measurement of energy transferred bythe power line, which can be inherently accurate for all significantharmonics, assuming the sampling rate satisfies the sampling theorem. Asdefined in ANSI/IEEE STD 100-1992, apparent power for a two terminalcircuit is:

    U.sub.x =E.sub.rms ×I.sub.rms

where E_(rms) and I_(rms) are the root-mean-square values of the voltageand current for the circuit. Thus, viewing voltage and currents on apower line as a composite of sinusoidal signals, apparent power (orapparent volt-ampere-hours) for all harmonics on a phase of a power linemay be determined by measuring RMS voltage and current.

Measurement of quadergy, however, is more problematic. The measurementof varhours conventionally has been accomplished either by using asecond meter in conjunction with a conventional watthour meter or, morerecently, a meter with the built-in capability of measuring bothwatthours and varhours. Typically, the technique for measuring varhoursinvolves phase-shifting the measured line voltage by 90° usingphase-shifting transformers (in analog meters) or time delay elements(in digital meters). Both of these methods may entail significant errorsarising from disregarding or failing to accurately shift all thesignificant harmonics of the voltage.

Metering based on arithmetic apparent volt-ampere-hours for the powerline has been proposed as an approximation of vector apparentvolt-ampere-hours. Arithmetic apparent power for a multi-phase systemrepresents the arithmetic sum of the magnitude of the apparent power foreach of the individual phases. Although relatively easy to compute,arithmetic apparent power tends to closely approximate vector apparentpower only in cases where the phases of the power line are balanced andsymmetric. Even in those cases, its measurement often leads tounexpected results under certain circumstances where the current orvoltage waveforms are nonsinusoidal. These characteristics tend to makearithmetic apparent power an unsuitable quantity for electricalmetering.

Conventional electricity meters and metering methods may fail to provideaccurate measurement of the actual cost of providing electrical energyto consumers where distortion is present. Increasing use of solid stateswitched motor drives, large switching power supplies and switched loadssuch as computers lead to distorted current waveforms, generallyaccompanied by a greater amount of associated distortion power.Distortion power increases demand on utility equipment and increasesenergy losses. Measures such as phasor volt-ampere-hours and arithmeticapparent volt-ampere-hours fail to rationally reflect these associatedcosts.

Errors arising from use of these conventional measurement techniqueswill become increasingly significant as the cost of delivering energyincreases. Utilities, driven by costs and the demands of their customersfor billing equity, have an increasing need for accurate metering whichreflects the true cost of delivering energy. In order to providecontinuity and minimize replacement costs, however, new equipment andmethods should be compatible with conventional meter connections andconventional metering formats, as well as with the various circuittopologies employed in electrical services.

SUMMARY OF THE INVENTION

In the light of the foregoing, it is therefore an object of the presentinvention to provide electricity meters and metering methods formetering of electricity on a power line having at least two conductivepaths.

It is another object of the present invention to provide electricitymeters and metering methods for metering of electricity which areaccurate for significant harmonics of the fundamental frequency of thepower line.

It is another object of the present invention to provide electricitymeters and metering methods for metering of electricity which arecompatible with conventional meter connections and capable of utilizingconventional metering formats.

It is another object of the present invention to provide electricitymeters and metering methods for metering of electricity which areadaptable to various power line circuit topologies.

These objects and advantages are provided by electricity meters andmetering methods for vector metering of electricity which sense linevoltage and line current signals on the power line, convert the sensedsignals into a digital signal, and compute vector metering quantitiesfor the power line over a determined interval of orthogonality for thesensed line voltages and line currents. Accordingly, accuratemeasurements of the vector metering quantity may be achieved. Thecomputed vector metering quantity may include vector apparentvolt-ampere-hours, vector apparent power, arithmetic apparentvolt-ampere-hours, arithmetic apparent power, phasor volt-ampere-hours,distortion volt-ampere-hours, distortion power, quadergy, reactivepower, energy, active power, power factor and distortion power factor.Vector computing means for computing vector metering quantities ispreferably implemented using a digital signal processor working incombination with a general-purpose microprocessor, integrated within anelectricity meter.

The present invention provides accurate and equitable measurement ofelectricity through accurate vector metering of electrical power. Thepresent invention also provides flexible, programmable metering whichallows billing of the metered customer based on combinations of meteredvector electrical quantities. The present invention also is easilyadaptable to different electrical service environments, such as 4-wirewye, 3-wire single phase, 3-wire delta and the like, without requiringcomponent changes or elaborate hardware modifications. Meterinstallation and power line maintenance are also aided.

In particular, vector metering of electricity is achieved in anelectricity meter according to the present invention by sensing linevoltage and line current signals on a power line. An interval oforthogonality for the sensed voltage and current signals is determinedfrom the sensed voltage signals. The sensed voltage and current signalsare converted into a digital signal from which a vector meteringparameter is computed for the interval of orthogonality using vectorcomputing means. Preferably, the sensed voltage and current signals areconverted into corresponding sequences of line voltage and line currentsamples, corresponding to a consecutive plurality of sampling timesspaced a sampling interval apart. Preferably, the sampling interval isuniform.

A digital phase-to-neutral voltage signal and corresponding phasecurrent signal may be computed from the digital signal prior tocomputing the vector metering quantity, thus defining a phase of thepower line with respect to a real or imputed neutral for the power line.Preferably, the digital phase-to-neutral voltage signal includes aseries of digital phase-to-neutral voltage samples, and the digitalphase current signal includes a series of digital phase current samples,each sample corresponding to the sampling time for the correspondingdigital line voltage sample or line current sample.

The interval of orthogonality is preferably determined by detecting thepassage of a predetermined integral number of cycles of a fundamentalfrequency reference signal which approximates the frequency of afundamental component of the voltages and currents on the power line.Preferably, an interval of orthogonality represents 60 cycles of thefundamental frequency reference signal for a nominal 60 Hz power system,or 50 cycles of the fundamental frequency reference signal for a nominal50 Hz system. The interval of orthogonality is preferably determined bynarrow-band filtering the computed phase-to-neutral voltage signals toproduce corresponding fundamental frequency phase-to-neutral voltagesignals. These fundamental frequency signals may be linearly combined toproduce the fundamental frequency reference signal.

According to one aspect of the present invention, computing a vectormetering quantity for the interval of orthogonality includes computingvector apparent volt-ampere-hours. Energy, quadergy and apparentvolt-ampere-hours are computed for each phase of the power line for theinterval of orthogonality. Vector-apparent volt-ampere-hours for theinterval of orthogonality are computed from the computed energy,quadergy and apparent volt-ampere-hours. Distortion volt-ampere-hoursfor each phase of the power line may be computed from these quantities.As will be understood by those skilled in the art, by computing energy,quadergy and distortion volt-ampere-hours over an interval oforthogonality, the computed energy, quadergy and distortionvolt-ampere-hour accurately represent vector components of the powerline. Vector algebra may be performed upon these components to yield anaccurate measurement of the vector apparent volt-ampere-hours for thepower line during the interval.

Quadergy is preferably computed by applying a reactive power filter tothe digital phase-to-neutral voltage signal and the digital phasecurrent signal. Preferably, this filter includes digital filtersimplemented in the vector computing means. The reactive power filterpreferably includes multiple phase-shifting filters and multiplierswhich produce two phase-shifted intermediate power product signals whichare summed to produce an output signal closely approximating thequadergy for the power line for all harmonics within a predeterminedfrequency range.

According to another aspect of the present invention, active, reactive,distortion and vector apparent power are computed for the power linefrom the computed energy, quadergy, distortion volt-ampere-hours andvector apparent volt-ampere-hours. Preferably, these vector quantitiesare computed by dividing the computed energy, quadergy, distortion orvector apparent volt-ampere-hours for the interval of orthogonality bythe number of sampling times occurring within the interval to yield thecorresponding power quantity. A power factor and a distortion powerfactor may also be computed from the computed energy, quadergy andapparent-volt-amperes per phase during the interval.

In another aspect of the present invention, a neutral current magnitudefor the power line is computed from the computed digital phase currentsignals. A neutral current status may be computed by comparing thecomputed neutral current magnitude to a predetermined threshold,indicating a unacceptable phase imbalance or other maintenancecondition. Similarly, an effective line voltage may be computed. A linevoltage status may be computed by comparing the computed effective linevoltage to an expected nominal operating voltage.

A phase angle associated with a fundamental frequency component of asensed line voltage signal may also be computed using a migratorydecimation technique. Samples of a narrow-band filtered version of adigital line voltage signal are selected over a series of consecutiveperiods of the fundamental frequency reference signal to obtain a set ofmigratory decimated samples. These samples preferably are selected suchthat a first selected migratory decimated sample coincides with a firstzero-crossing of the fundamental frequency reference signal. The nextselected migratory decimated sample is selected from the next period ofthe fundamental frequency reference signal, delayed a predeterminedmigratory decimation interval from the point on the fundamentalfrequency reference signal waveform at which the preceding sample wastaken. Samples are similarly taken from succeeding intervals, thusyielding a set of migratory decimated samples approximating a period ofthe digital voltage signal. Fourier analysis is applied to thesemigratory decimated samples to compute the phase angle of thefundamental frequency component of the line voltage signal with respectto the reference signal. Thus an accurate measurement of line voltagephase angle is provided, useful for meter installation and maintenance,among other tasks.

In another aspect of the present invention, metering quantities for aninterval of orthogonality may be cumulatively recorded, analyzed forminimum and maximum values over a period of interest, and subjected toother analyses for billing and other purposes. An identified meteringquantity may be computed, based on an associated detent. Vector meteringquantities may also be computed notwithstanding the loss of a sensedline voltage signal, thus providing a means for estimating power when avoltage transformer or other component has failed.

Accordingly, vector electricity meters and methods for vector meteringof electricity are provided which can accurately measure vector meteringquantities. These meters and methods provide for metering of electricitywhich accurately and equitably reflects the costs of delivering energyto customers. These meters and methods are also adaptable to variouspower line circuit topologies, and are compatible with conventionalmeter connections and formats.

BRIEF DESCRIPTION 0F THE DRAWINGS

FIG. 1 is a schematic diagram illustrating a vector electricity meteraccording to the present invention.

FIG. 2 is a schematic block diagram illustrating a vector electricitymeter housed within a meter case according to the present invention.

FIG. 3A is a block diagram illustrating operations in a vectorelectricity meter according to the present invention.

FIG. 3B is a block diagram illustrating conversion of sensed linevoltage and current signals to digital samples according to the presentinvention.

FIG. 4 is a block diagram illustrating operations in a vectorelectricity meter according to the present invention.

FIG. 5 is a block diagram illustrating determination of an interval oforthogonality according to the present invention.

FIG. 6 is a block diagram illustrating computation of a vector meteringquantity from sensed line voltage and current signals according to thepresent invention.

FIG. 7 is a block diagram illustrating operations for computing aphase-to-neutral voltage signal and a phase current signal to define aphase of a power line according to the present invention.

FIG. 8 is a block diagram illustrating computation of a vector meteringquantity based on an indicated circuit topology.

FIG. 9 is a table illustrating exemplary operations for computingphase-to-neutral voltage samples and phase current samples based on anindicated circuit topology according to the present invention.

FIG. 10 is a block diagram illustrating operations for computing energyper phase during an interval of orthogonality according to the presentinvention.

FIG. 11 is a block diagram illustrating operations for computingapparent volt-ampere-hours per phase for an interval of orthogonalityaccording to the present invention.

FIG. 12A is a block diagram illustrating a reactive power filteraccording to the present invention.

FIG. 12B graphically illustrates a transfer function for a reactivepower filter according to the present invention.

FIG. 13 is a block diagram illustrating operations for computingquadergy per phase for an interval of orthogonality according to thepresent invention.

FIG. 14 is a block diagram illustrating operations for computing vectorapparent volt-ampere-hours for a power line for an interval oforthogonality according to the present invention.

FIG. 15A is a block diagram illustrating operations for computing a linevoltage phase angle according to the present invention.

FIG. 15B is a block diagram illustrating decimated sampling for phaseangle computation according to the present invention.

FIG. 16A is a block diagram illustrating operations for computing anexpected nominal line voltage according to the present invention.

FIG. 16B is a block diagram illustrating operations for computing aneffective line voltage according to the present invention.

FIG. 17 is a block diagram illustrating operations for computing a linevoltage status according to the present invention.

FIG. 18 is a block diagram illustrating operations for computing aneutral current magnitude and neutral current status according to thepresent invention.

FIG. 19 graphically illustrates power vector relationships.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention now will be described more fully hereinafter withreference to the accompanying drawings, in which preferred embodimentsof the invention are shown. This invention may, however, be embodied inmany different forms and should not be construed as limited to theembodiments set forth herein; rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art. Likenumbers refer to like elements throughout.

FIGS. 6-7, 10-11, 13-15A and 16A-18 are flowchart illustrations ofmethods and systems according to the invention. It will be understoodthat each block of the flowchart illustrations, and combinations ofblocks in the flowchart illustrations, can be implemented by computerprogram instructions. These computer program instructions may be loadedonto a computer or other programmable apparatus to produce a machine,such that the instructions which execute on the computer or otherprogrammable apparatus create means for implementing the functionsspecified in the flowchart block or blocks. These computer programinstructions may also be stored in a computer-readable memory that candirect a computer or other programmable apparatus to function in aparticular manner, such that the instructions stored in thecomputer-readable memory produce an article of manufacture includinginstruction means which implement the function specified in theflowchart block or blocks. The computer program instructions may also beloaded onto a computer or other programmable apparatus to cause a seriesof operational steps to be performed on the computer or otherprogrammable apparatus to produce a computer implemented process suchthat the instructions which execute on the computer or otherprogrammable apparatus provide steps for implementing the functionsspecified in the flowchart block or blocks.

Accordingly, blocks of the flowchart illustrations support combinationsof means for performing the specified functions and combinations ofsteps for performing the specified functions. It will also be understoodthat each block of the flowchart illustrations, and combinations ofblocks in the flowchart illustrations, can be implemented by specialpurpose hardware-based computer systems which perform the specifiedfunctions or steps, or combinations of special purpose hardware andcomputer instructions.

A Vector Electricity Meter

FIG. 1 and 2 illustrate a vector electricity meter according to thepresent invention. Voltage sensor 110 and current sensor 120 sensevoltage and current signals on a power line and input the sensedvoltages and currents 315 into converting means 320. Converting means320, such as an analog-to-digital converter (A/D), may include signalprocessing circuits for rejecting DC components in the sensed voltagesand currents 315, compensating for phase shifts induced by sensingmeans, and the like, as well as means for sampling the sensed voltagesand currents to obtain a digital signal 325.

The digital signal 325 is input into vector computing means 330, shownin FIG. 1 as including a computer program running on a digital signalprocessor 130, a microcomputer 140 and a program/data memory 150.Preferably, digital signal processor (DSP) 130 performs vector powercomputations based on the digital signal 325, under the control of themicrocomputer 140. Digital signal processor 130 preferably is ahigh-speed processing device having a highly parallel architecture whichquickly performs repetitive calculations. Examples of digital signalprocessor 130 are devices in Texas Instruments Corporation's TMS320xline of digital signal processors. In addition to controlling digitalsignal processor 130, the microcomputer 140 may control other peripheraldevices, such as a display 160 or a communications interface 170. Thoseskilled in the art will understand that computing means 330 may beimplemented using various combinations of hardware and softwareelements, including other digital signal processing devices or generalpurpose processors.

Sensing means 310, converting means 320 and vector computing means 330preferably are integrated within a standard-type electricity meter 200,as shown in FIG. 2. Meter 200 may include an LCD display 160 and anoptical port 170 for communicating metering data to a data recorder orother device. Meter 200 may be directly connected to conductors 220A-Cof a power line 210 directly for low-voltage, low-power installations,or may be buffered through the use of voltage and current transformers,as is well-known to those skilled in the art.

Vector Electricity Metering--Overview

It will be understood by those skilled in the art that vector apparentpower (or vector apparent volt-ampere-hours) for a power line havingmore than one conducting path may be determined by first determining itsthree orthogonal components: active power (or energy); reactive power(or quadergy); and distortion power (or distortion volt-ampere-hours).In vector terms: ##EQU1## In a vector electricity meter according to thepresent invention, these components are computed over an interval oforthogonality for the sinusoidal components of the periodic voltages andcurrents on the power line.

Those skilled in the art will understand that an n-dimensional vector ycan be represented as a sum of basis vectors x₁, x₂, . . . , x_(n) :

    y=c.sub.1 x.sub.1 +c.sub.2 x.sub.2 +. . . +c.sub.n x.sub.n.(1)

If the basis vectors are orthogonal, the inner products of the basisvectors are equal to zero:

    <x.sub.i,x.sub.j >,i≠j.

Forming the inner product of a basis vector x_(i) with both sides ofEquation (1) produces: ##EQU2## Thus, a vector can be convenientlyexpressed using an orthogonal basis because the coordinates c_(i) can beeasily calculated.

The relationship between orthogonality and inner products applies tofunctions in general. The inner product of two functions may be definedas an integral over an interval: ##EQU3## As with the basis vectors, theinner product of the two functions is zero if the functions areorthogonal:

    <g.sub.i (t),g.sub.j (t)>=0,i≠j.

The interval (t₁, t₂) is an interval of orthogonality for the functionsg_(i) (t) and g_(j) (t). A function can be expressed as a sum oforthogonal functions over the interval of orthogonality (t₁, t₂):

    f(t)=c.sub.1 g.sub.1 (t)+c.sub.2 g.sub.2 (t)+. . . +c.sub.n g.sub.n (t).

Thus, a function represented as a sum of orthogonal functions over aninterval of orthogconality can be determined using "vector algebra."

In order to accurately perform vector algebra using measured values forenergy, quadergy and apparent volt-ampere-hours for each phase of apower line, these vector metering components preferably are measured foran interval of orthogonality so that the vector sum of these vectormetering components is an accurate representation of vector apparentvolt-ampere-hours, i.e., the inner products of voltage and current arezero. For a power line having voltages and currents including asinusoidal fundamental frequency component and multiple harmonicsthereof, an interval of orthogonality for all the sinusoidal voltagesand currents is an integral number of cycles of the fundamentalfrequency component.

Having explained why vector metering components preferably arecalculated over an interval of orthogonality, operations for vectormetering according to the present invention will now be explained. FIG.3A is a block diagram illustrating basic operations for vector meteringaccording to the present invention. Line voltage and line currentsignals are sensed on the power line by voltage sensor 110 and currentsensor 120. In converting means 320, the sensed line voltage and linecurrent signals 315 are converted into a digital signal 325. The digitalsignal 325 is then input into vector computing means 330, where a vectormetering quantity is computed from the digital signal 325.

As shown in FIG. 3B, in converting means 320 a digital signal 325 isproduced, preferably in the form of series of digital line voltagesamples 326 and line current samples 327. The sensed voltages andcurrent signals 315 are sampled in sampling means 321 at predeterminedsampling intervals to produce a plurality of line voltage and currentsamples 322. The voltage and current samples are converted intocorresponding series of digital line voltage samples 326 and digitalline current samples 327 in sample converting means 323. It will beunderstood by those skilled in the art that in order to accuratelycompute vector metering quantities for a power line from a fundamentalfrequency of 60 Hz up to the twenty-third harmonic of the fundamental,or 1380 Hz, the sampling rate must be greater than 2760 samples persecond. Preferably, the digital line voltage samples 326 and the digitalline current samples 327 represent samples taken at a sampling rate of3900 samples per second, or a sampling interval of approximately 26microseconds.

According to the present invention, the vector computing means 330 ofFIG. 1 and vector computing operation 330 of FIG. 3A may resolve thesensed line voltages and current signals 315 into equivalent three-phasequantities. As illustrated in FIG. 7, phases preferably are defined forthe power line at Block 700 by taking a digital line voltage samplee_(k) and a corresponding digital line current sample i_(k) at Block710, computing a digital phase-to-neutral voltage sample at Block 720,and computing a digital phase current sample at Block 730.

The computations of Blocks 720 and 730 are dependent upon the circuittopology of the power line. As illustrated in FIG. 8, circuitidentifying means 810 for identifying a circuit topology are provided,with vector computing means 330 performing corresponding calculations ofthe digital phase-to-neutral voltage signals and the digital phasecurrent signals based on the indicated circuit topology. Those skilledin the art will understand that circuit identifying means 810 mayinclude memory elements, select resistors, DIP switch settings and thelike. Exemplary computations for the vector computing means 330 of FIG.3B for different circuit topologies are illustrated in the table of FIG.9. For the table, V_(a), V_(b) and V_(c) represent digital line voltagesamples 326, I_(a), I_(b) and I_(c) represent corresponding digital linecurrent samples 327, while V_(a0), V_(b0) and V_(c0) represent thecorresponding computed digital phase-to-neutral voltage samples andI_(a0), I_(b0) and I_(c0) represent the corresponding computed digitalphase current samples.

FIG. 4 illustrates the vector electricity meter of FIGS. 1 and 3A, withthe addition of interval determining means 420 for determining aninterval of orthogonality for voltage and current signals on the powerline. As discussed above, vector power computations are performed overan interval of orthogonality for voltage and current signals on thepower line. Vector computing means 330 may compute a vector meteringquantity for the interval of orthogonality determined by intervaldetermining means 420.

FIG. 5 illustrates operations to determine an interval of orthogonalityfrom the sensed voltage and current signals 315 for use by vectorcomputing means 330. A fundamental frequency reference signal 535 isproduced having a frequency approximately equivalent to the fundamentalfrequency of the sensed line voltage and current signals 315. In orderto produce the fundamental frequency reference signal 535, aphase-to-neutral voltage signal 715 defining a phase of the power lineis produced from the sensed line voltage signals 315 in producing means510. The digital phase-to-neutral voltage signal for each phase is inputto a narrow-band filter 520 preferably having a passband approximatelycentered on the nominal fundamental frequency of the power line toproduce a fundamental frequency voltage signal 525.

The fundamental frequency voltage signals 525 produced are combined inlinear combining means 530, which perform a weighted combination of thesignals. Preferably, a first fundamental frequency voltage signal isscaled by approximately one-half, a second fundamental frequency voltagesignal is scaled by approximately one-fourth and a third fundamentalfrequency voltage signal is scaled by approximately one-eighth, and thescaled signals summed to produce the fundamental frequency referencesignal 535. The resulting signal has approximately the same fundamentalfrequency as the fundamental frequency voltage signals 525, and remainspresent even if one of the fundamental frequency voltage signals is notpresent, as in cases such as, for example, metering a three-wire singlephase power line or a three-phase power line for which one line voltageis missing.

For a power line characterized by a fundamental frequency and multipleharmonics thereof, a common interval of orthogonality for the voltagesand currents on the power line is an interval equivalent to an integralnumber of cycles of the lowest frequency component, i.e., an integralnumber of cycles of the fundamental. Thus, an interval of orthogonalityfor the power line may be determined by detecting means 540 detectingthe passage of a predetermined number of cycles of the digitalfundamental frequency reference signal 535. Preferably, thepredetermined number of cycles of the fundamental frequency referencesignal 535 used to determine the interval of orthogonality is such thata long enough interval is provided to allow computations for eachinterval to be completed before computations for the succeeding intervalcommence, without making the interval so long as to cause variousaccumulations performed in vector computing means 330 to overflow.Typically, for a nominal 60 Hz power line, 60 cycles of the fundamentalfrequency reference signal 535, or nominally one second, define aninterval of orthogonality according to the present invention. Similarly,for a nominal 50 Hz power line, 50 cycles of the fundamental frequencyreference signal 535 define an interval. It will be understood by thoseskilled in the art that other integral numbers of cycles of thefundamental frequency reference signal 535 may be used with the presentinvention, however.

It will be understood by those skilled in the art that functions ofproducing means 510, narrow-band filtering means 520, linear combiningmeans 530 and detecting means 540 may be integrated with vectorcomputing means 330, for example, in the digital signal processor 130 ofFIG. 1. Those skilled in the art will also understand that theseelements may also be implemented separately in analog circuits, digitalcircuits and combinations thereof. For example, producing means 510 mayinclude a resistor network, narrow-band filter 520 may include an analogbandpass filter, linear combining means 530 may include analogarithmetic circuits and detecting means 540 may include an analogzero-crossing detector and associated counter which provides aninterrupt or other signal to vector computing means 330 to indicate aninterval of orthogonality.

Computing Power-Related Vector Metering Quantities

Having described a vector electricity meter and basic operationsthereof, this section illustrates the computation of variouspower-related vector metering quantities in the vector computing means330 of FIGS. 1 and 3A. As an example of computing a power-related vectormetering quantity, FIG. 6 illustrates basic operations for computingvector apparent power for an interval of orthogonality from energy,quadergy and apparent volt-ampere-hours computed for each phase of thepower during the interval. FIGS. 10, 11, 13 and 14 illustrate detailedoperations for computing energy per phase, quadergy per phase, apparentvolt-ampere-hours per phase, and vector apparent volt-ampere-hours forthe power line during the interval, respectively. FIGS. 12A-12Billustrate a reactive power filter for computing quadergy per phaseaccording to the present invention, and operations for implementing thereactive filter in vector computing means 330.

Referring to FIG. 6, energy per phase, quadergy per phase, and apparentvolt-ampere-hours per phase are computed for the interval oforthogonality at Blocks 610, 620, 630, respectively. Vector apparentvolt-ampere-hours for the power line for the intrerval are computed atBlock 640 from the computed energy, quadergy, and apparentvolt-ampere-hours for the phases. Typically, distortion volt-amperehours are computed from the computed energy, quadergy, and apparentvolt-ampere-hours per phase: ##EQU4## Energy, quadergy and distortionvolt-ampere-hours for the power line during the interval may be computedby summing the computed energy, quadergy and distortionvolt-ampere-hours per phase. Vector apparent volt-ampere-hours for thepower line during the interval may be computed from the computed energy,quadergy and distortion volt-ampere-hours. Those skilled in the art willunderstand, however, that although these computations may be performedindividually, they may also be combined in composite computations.

FIG. 10 illustrates operations to compute energy per phase for aninterval of orthogonality according to the present invention (Block1000). A digital phase-to-neutral voltage sample e_(k) obtained at Block1010 is multiplied by the corresponding digital phase current samplei_(k) at Block 1020. The product of the voltage and current samples foreach sampling time is accumulated at Block 1030. After the end of theinterval of orthogonality at Block 1040, the accumulated product of thevoltage and samples is multiplied by the number of samples N_(s) and thesampling interval T_(s) to compute the energy transferred by the powerline during the interval of orthogonality at Block 1050.

FIG. 11 illustrates operations to compute apparent volt-ampere-hours perphase according to the present invention (Block 1100). A digitalphase-to-neutral voltage sample e_(k) obtained at Block 1110 is squaredat Block 1120, and the resulting product is added at Block 1140 to a sumof the previous squared digital phase-to-neutral voltage samples.Similarly, a digital phase current sample i_(k) obtained at Block 1110is squared at Block 1130 and the resulting product accumulated at Block1150. After the end of an interval at Block 1160, the accumulatedsquared digital phase-to-neutral voltage samples and the accumulatedsquare digital phase current samples for each phase from the intervalare multiplied at Block 1170 by the square of the number of samplesN_(s) times the sampling interval T_(s) to produce a quantity equivalentto the square of the apparent volt-ampere-hours for the phase during theinterval of orthogonality. The apparent volt-ampere-hours for the phaseduring the interval is computed at Block 1180 by taking the square rootof this product.

FIG. 12A illustrates a reactive power filter 1210 for computing reactivepower according to the present invention. It will be understood by thoseskilled in the art that in order to accurately measure reactive power ofa phase for all significant harmonics using a phase-shifted form of aphase voltage signal to multiply a corresponding phase current signal,the phase voltage signal must be shifted equally for all of thoseharmonics. Conventional varhour meters typically cannot achieve such auniform shift, usually correctly shifting only the fundamental andcertain other frequency components

A uniform phase shift is achieved according to the present invention fora desired frequency band by inputting the phase voltage signal E and thephase current signal I into a reactive power filter 1210. Firstphase-shifting filter H₁ and second phase-shifting filter H₃ preferablyare recursive digital filters which induce a first phase shift δ₁.Similarly, second phase-shifting filter H₂ and fourth phase-shiftingfilter H₄ similarly preferably are recursive digital filters whichinduce a second phase shift δ₂. The outputs from each of these filtersare multiplied as shown and summed to produce an output signal Q', whichrepresents a product of a function of frequency and the reactive powerQ:

    e(t)→E∠α;

    i(t)→I∠β;

    H.sub.1 (f)=H.sub.3 (f)=G.sub.1 ∠δ.sub.1 ;

    H.sub.2 (f)=H.sub.4 (f)=G.sub.2 ∠δ.sub.2 ;

    A=G.sub.1 G.sub.2 [EI cos(β-α)cos(δ.sub.2 -δ.sub.1)-EI sin(β-α)sin(δ.sub.2 -δ.sub.1)];

    A=G.sub.1 G.sub.2 [P cos(δ.sub.1 -δ.sub.2)-Q sin(δ.sub.1 -δ.sub.2)];

    B=G.sub.1 G.sub.2 [EI cos(β-α)cos(δ.sub.1 -δ.sub.2)-EI sin(β-α)sin(δ.sub.1 -δ.sub.2)];

    B=G.sub.1 G.sub.2 [P cos(δ.sub.1 -δ.sub.2)+Q sin(δ.sub.1 -δ.sub.2)];

and

    Q'=GB-GA=2GG.sub.1 G.sub.2 sin(δ.sub.1 -δ.sub.2)Q.

It will be understood by those skilled in the art that if G₁, G₂ and Gare unity, the result reduces to:

    Q'=2 sin(δ.sub.1 -δ.sub.2)

or

    Q'=g(f)Q.

Transfer characteristics for the function g(f)/2 is shown in FIG. 12B.The transfer functions of the phase-shifting filters H₁, H₂, H₃ and H₄are chosen such that the phase difference closely approximates 90degrees over a band of frequencies Δf, thus making the sine of the phasedifference δ₁ -δ₂ approximately unity and the output of the filter Q' aclose approximation of the reactive power over the frequency range.Preferably, Δf spans the range of significant harmonics of thefundamental frequency of the phase voltage and current signalspreferably up to and including the twenty-third harmonic. Output Q' maybe integrated to yield an accurate measurement of quadergy.

Those skilled in the art will understand that the reactive power filter1210 may be implemented using analog circuitry, specialized digitalcircuitry or by software running on general-purpose processors. FIG. 13illustrates operations for implementing the reactive power filter 1210of FIG. 12A, which may be performed in the vector computing means 330 ofFIG. 3A (Block 1300). A first phase-shifting filter is applied to adigital phase-to-neutral voltage sample e_(k) obtained at Block 1305 tocompute a first phase-shifted digital phase-to-neutral voltage samplee_(k) ' at Block 1310. A second phase-shifting filter is also applied toshe digital phase-to-neutral voltage sample e_(k) to compute a secondphase-shifted digital phase-to-neutral voltage sample e_(k) " at Block1315. Similarly, a third phase-shifting filter having the same transferfunction as the first phase-shifting filter is applied to acorresponding digital phase current sample i_(k) obtained at Block 1305to compute a first phase-shifted digital phase current sample i_(k) ' atBlock 1320. A fourth phase-shifting filter having the same transferfunction as the second phase-shifting filter is also applied to thedigital phase current sample i_(k) to compute a second phase-shifteddigital phase current sample i_(k) " at Block 1325.

The second phase-shifted digital phase-to-neutral voltage sample ismultiplied by the first phase-shifted phase current sample to compute afirst intermediate power sample q_(k) ' at Block 1330, and the firstphase-shifted digital phase-to-neutral voltage sample is multiplied bythe second phase-shifted phase current sample to compute a secondintermediate power sample q_(k) " at Block 1335. The second intermediatepower sample is subtracted from the first intermediate power sample tocompute a reactive power sample q_(k) at Block 1340. The reactive powersamples are accumulated at Block 1345. At the end of the interval atBlock 1350, the accumulated reactive power samples are multiplied atBlock 1355 by the number of samples N_(s) and the sampling intervalT_(s) to compute the quadergy for the phase during the interval.

FIG. 14 illustrates detailed operations to compute vector apparentvolt-ampere-hours from the computed energy, quadergy and apparentvolt-ampere-hours for the phases of the power line (Block 1400). At theend of an interval of orthogonality at Block 1410, the accumulatedenergy and quadergy for each defined phase of the power line aresubtracted as vectors at Block 1420 from the apparent volt-ampere-hoursfor the phase for the interval to compute the distortionvolt-ampere-hours for the phase for the interval. Energy, quadergy anddistortion volt-ampere-hours are computed for power line by summing atBlocks 1430, 1440 and 1450, respectively, the computed values for thesequantities for all the phases of the power line. Vector apparentvolt-ampere-hours is computed at Block 1460 as the square root of thesum of the squares of the energy, quadergy and distortionvolt-ampere-hours.

According to the present invention, vector metering quantities computedusing the vector computing means 330 of FIG. 3A may include energy,quadergy, distortion power, and corresponding per phase meteringquantities. As will be understood by those skilled in the art, variouspower factors such as a power factor, a distortion power factor and thelike may also be computed from ratios of the various meteringquantities.

Vector computing means 330 may also compute related power quantities.Vector computing means 330 preferably stores the number of samples takenduring an interval of orthogonality, thus providing a measure of thelength of the interval. Vector apparent power may be computed from thevector apparent volt-ampere-hours computed for the interval oforthogonality by dividing the computed vector apparent volt-ampere-hoursby the length of the interval. Similarly, active power may be computedfrom the computed energy for the interval by dividing the computedenergy by the length of the interval and reactive power may be computedfrom the computed quadergy by dividing the computed quadergy by thelength of the interval.

It will be understood by those skilled in the art that the computationof vector metering quantities in vector computing means 330 is notlimited to the computing steps of the illustrated embodiments. Forinstance, according to the present invention, vector apparent power maybe computed without first computing vector apparent volt-ampere-hours byfirst computing active, reactive and distortion power for the intervalof orthogonality from the energy, quadergy and apparentvolt-ampere-hours for the phases of the power line, and then vectorsumming these components. Vector apparent volt-ampere-hours may becomputed from vector apparent power for the orthogonal interval bymultiplying the computed vector apparent power for the interval by thenumber of samples in the interval.

Electric utilities often bill their customers based on energy plus anadditional quantity, such as quadergy or phasor volt-ampere-hours.Typically, a "detent" is also applied to the measurement of thesequantities, e.g., the utility may choose to bill only for deliveredenergy, for both delivered and received energy, lagging quadergy, andthe like. Vector computing means 330 may compute an identified vectormetering quantity to be metered. The identified metering quantity may beidentified to vector computing means 330 for example, by a meteringtechnician through the communications interface 170 illustrated inFIG. 1. Those skilled in the art will understand that the identifiedquantity may include an associated detent, such as leading quadergyonly, received and delivered energy, and the like.

Computing Other Vector Metering Quantities

The vector computing means 330 illustrated in FIG. 3A may also computeother vector metering quantities useful for power system safety andmaintenance, meter installation and the like, such as a phase angle, aneffective line voltage, an expected nominal operating voltage, a linevoltage status, a neutral current magnitude, and a neutral currentstatus. FIGS. 15A-15B illustrate operations for computing a phase angleof a sensed line voltage 315 with respect to the fundamental frequencyreference signal 535 of FIG. 5. FIGS. 16A-B illustrate operations forcomputing an effective line voltage and an expected nominal operatingvoltage. FIG. 17 illustrates operations for using the computed effectiveline voltage to compute a line voltage status. Finally, FIG. 18illustrates operations for computing a neutral current magnitude and aneutral current status.

Operations for determining a phase angle of a sensed line voltage signal315 with respect to the fundamental frequency reference signal 535 (seeFIG. 5) are illustrated in FIGS. 15A-15B. Digital line voltage samplesobtained at Block 1510 are narrow-band filtered at Block 1520 to computea series of digital fundamental frequency line voltage samplesrepresenting a fundamental frequency component signal of the sensed linevoltage signal. A set of migratory decimated digital line voltagesamples are selected at Block 1530, one each from a succession of cyclesof the fundamental frequency reference signal 535.

In particular, as illustrated in FIG. 15B, each migratory decimatedsample is selected such that it comes from a sampling time delayed apredetermined decimation interval N₁ from the previous decimated samplewith respect to the fundamental frequency reference signal 535.Preferably, the first decimated sample e_(d1) is the first samplefollowing the start of the interval of orthogonality, illustrated inFIG. 18B as following a first zero crossing of the fundamental frequencyreference signal 535. The next decimated sample e_(d2) is selected fromsamples taken during the next cycle of the fundamental frequencyreference signal 535, delayed the decimation interval N₁ from the pointon the waveform of the fundamental frequency reference signal 535 wherethe preceding sample e_(d1) was selected.

Preferably, the decimation interval N₁ is such that the set of decimatedsamples selected during an interval of orthogonality approximatelyrepresent a period of the fundamental frequency component signal of thesensed line voltage signal 315. For a 60 Hz power line sampled at 3900samples per second, for example, approximately 65 samples are taken in acycle. If the migratory decimated samples are selected from successivecycles of the fundamental frequency reference signal 535 such that eachis delayed a decimation interval N₁ of 13 samples from the precedingsample with respect to the fundamental frequency reference signal, a setof 5 decimated samples may be selected during an interval of 60 cyclesof the fundamental frequency reference signal 535, thus approximating aperiod of the fundamental frequency component signal of the sensed linevoltage 315. For a 50 Hz system at the same sampling rate and decimationinterval N₁, the waveform may be represented by 6 samples.

The phase angle of the fundamental component of the line voltage may becomputed after an interval of orthogonality at Block 1540 using Fourieranalysis at Block 1550. Those skilled in the art will understand that##EQU5## are the cosine and sine terms, respectively, of the Fourierseries representation of the fundamental frequency component signal ofthe sensed line voltage signal 315, based on M migratory decimatedsamples. For these equations, N_(s) is the number of samples takenduring an interval of orthogonality, N_(c) is the nominal fundamentalfrequency of the power line (50 or 60 Hz), N₁ is the decimationinterval, and f_(s) is the sampling frequency.

The vector computing means 330 of FIGS. 1 and 3A may also compute aneffective line voltage and a nominal expected operating voltage for thepower line from a sensed line voltage signal 315, and monitor the sensedline voltage signals 315 based on the computed expected nominaloperating voltage. Operations for computing an expected nominaloperating voltage are illustrated in FIG. 16A (Block 1600). Theeffective voltage of a sensed line voltage signal 315 is computed atBlock 1610 for an interval of orthogonality, preferably soon after orduring an initialization of vector computing means 330. A phase anglefor the line voltage may also be computed at Block 1500, also preferablyduring an initialization or soon thereafter. The expected nominaloperating voltage is selected at Block 1620 from predetermined nominaloperating voltages 1630 based on the computed effective voltage and thecomputed phase angle. Preferably, the selected expected nominaloperating voltage is the predetermined nominal operating voltage 1630closest to the computed effective voltage. The predetermined nominaloperating voltages 1630 preferably include standard line voltages suchas 120 volts, 240 volts, 277 volts and the like.

The expected nominal operating voltage may also be computed based on thecomputed phase angle. For example, the computed effective voltage mayfall approximately equally between two predetermined nominal operatingvoltages, such as 240 volts and 277 volts, which typically correspond toa three-wire single phase service and a four-wire three phase wyeservice, respectively. As will be understood by those skilled in theart, these two circuit topologies may be differentiated by the differentphase angles between the line voltages, i.e., the line voltages in the277 volt service typically will be separated by a nominal phase angle of120 degrees while the line voltages of the 240 volt service typicallyare separated by a nominal 60 degrees. Vector computing means 330 maycompute the expected nominal operating voltage by selecting thepredetermined nominal operating voltage having a phase anglecharacteristic closest to the computed phase angle.

FIG. 16B illustrates detailed operations for computing an effective linevoltage (Block 1610). Line voltage samples obtained at Block 1611 arenarrow-band filtered at Block 1612, the filtered samples squared atBlock 1613, and the squared samples accumulated at Block 1614. After theend of the interval at Block 1615, the effective voltage during theinterval is computed by taking the square root of the accumulateddigital line squared voltage samples divided by the number of samplesN_(s) times the sampling interval T_(s) at Block 1616.

Referring now to FIG. 17, the computed expected nominal line voltage maybe used to compute at a line voltage status (Block 1700). At Block 1710an effective line voltage is computed. The computed line voltage statusis compare to an expected nominal operating voltage, based onpredetermined tolerance 1740, to compute a line voltage status at Block1720. It will be understood by those skilled in the art that althoughthe status computed preferably relates to an overvoltage or undervoltagecondition on the power line, other line voltage status may be computed,such as statistical deviation of the computed effective voltage withrespect to the expected nominal operating voltage and the like. It willalso be understood that the computed status may be communicated fromvector computing means 330 to a user, a switchgear control system, andthe like, for maintenance, shutdown and other purposes, for example,through the communications interface 170 or display 160 of FIG. 1. Itwill be also be understood that effective line voltage and line voltagestatus may be computed at every interval of orthogonality or at otherpredetermined intervals.

Referring now to FIG. 18, vector computing means 330 may also computeand monitor a neutral current magnitude from computed digital phasecurrent samples (Block 1800). Digital phase current samples obtained foreach phase at Block 1810 are summed at Block 1820 and the sum squared atBlock 1830. The neutral current magnitude is computed by taking thesquare root of the squared sum at Block 1830. A neutral current statusmay be computed at Block 1840 by comparing the computed neutral currentmagnitude to a predetermined threshold 1842. It will be understood bythose skilled in the art that the computed status may be communicated toa user, a switchgear control system, and the like, for maintenance,shutdown and other purposes. It will also be understood that neutralcurrent magnitude and status may be computed at every sample time, atevery interval of orthogonality, or at other predetermined intervals.

In the drawings and specification, there have been disclosed typicalpreferred embodiments of the invention and, although specific terms areemployed, they are used in a generic and descriptive sense only and notfor purposes of limitation, the scope of the invention being set forthin the following claims.

That which is claimed:
 1. A method for measuring reactive power for anelectrical power line, comprising the steps of:sensing a voltage signaland a current signal on the power line; phase-shifting the voltagesignal according to a first phase shift to obtain a first phase-shiftedvoltage signal; phase-shifting the voltage signal according to a secondphase shift to obtain a second phase-shifted voltage signal;phase-shifting the current signal according to the first phase shift toobtain a first phase-shifted current signal; phase-shifting the currentsignal according to the second phase shift to obtain a secondphase-shifted current signal; multiplying the first phase-shiftedvoltage signal by the second phase-shifted current signal to obtain afirst intermediate power product signal; multiplying the secondphase-shifted voltage signal by the first phase-shifted current signalto obtain a second intermediate power product signal; and summing thefirst intermediate power product signal and the second intermediatepower product signal to obtain an output signal representing reactivepower for the power line over a predetermined frequency range.
 2. Amethod according to claim 1:wherein said step of phase-shifting thevoltage signal according to a first phase shift comprises the step ofapplying a first phase-shifting filter having a firstphase-versus-frequency transfer function to the voltage signal to obtaina first phase-shifted voltage signal; wherein said step ofphase-shifting the voltage signal according to a second phase shiftcomprises the step of applying a second phase-shifting filter having asecond phase-versus frequency transfer function to the voltage signal toobtain a second phase-shifted voltage signal, the secondphase-versus-frequency transfer function differing from the firstphase-versus-frequency transfer function by approximately 90 degreesover the predetermined frequency range; wherein said step ofphase-shifting the current signal according to the first phase shiftcomprises the step of applying a third phase-shifting filter having thefirst phase-versus-frequency transfer function to the current signal toobtain a first phase-shifted current signal; and wherein said step ofphase-shifting the current signal according to the second phase shiftcomprises the step applying a fourth phase-shifting filter having thesecond phase-versus-frequency transfer function to the phase-to-neutralcurrent signal to obtain a second phase-shifted current signal.
 3. Asystem for measuring reactive power for an electrical power line,comprising:a voltage sensor which senses a voltage on the power line; acurrent sensor which senses a current signal on the power line; firstphase-shifting means, responsive to said voltage sensor, forphase-shifting the voltage signal according to a first phase shift toobtain a first phase-shifted voltage signal; second phase-shiftingmeans, responsive to said voltage sensor, for phase-shifting the voltagesignal according to a second phase shift to obtain a secondphase-shifted voltage signal; third phase-shifting means, responsive tosaid current sensor, for phase-shifting the current signal according tothe first phase shift to obtain a first phase-shifted current signal;fourth phase-shifting means, responsive to said current sensor, forphase-shifting the current signal according to the second phase shift toobtain a second phase-shifted current signal; a first multiplier,responsive to said first phase-shifting means and to said fourthphase-shifting means, which multiplies the first phase-shifted voltagesignal by the second phase-shifted current signal to obtain a firstintermediate power product signal; a second multiplier, responsive tosaid second phase-shifting means and to said third phase-shifting means,which multiplies the second phase-shifted voltage signal by the firstphase-shifted current signal to obtain a second intermediate powerproduct signal; and an adder, responsive to said first multiplier and tosaid second multiplier, which sums the first intermediate power productsignal and the second intermediate power product signal to obtain anoutput signal representing reactive power for the power line over apredetermined frequency range.
 4. A system according to claim 3:whereinsaid first phase-shifting means comprises a first phase-shifting filterhaving a first phase-versus-frequency transfer function; wherein saidsecond phase-shifting means comprises a second phase-shifting filterhaving a second phase-versus frequency transfer function, the secondphase-versus-frequency transfer function differing from the firstphase-versus-frequency transfer function by approximately 90 degreesover the predetermined frequency range; wherein said thirdphase-shifting means comprises a third phase-shifting filter having thefirst phase-versus-frequency transfer function; and wherein said fourthphase-shifting means comprises a fourth phase-shifting filter having thesecond phase-versus-frequency transfer function.
 5. A system accordingto claim 4:wherein said first phase-shifting filter comprises a firstrecursive digital filter having a first phase-versus-frequency transferfunction; wherein said second phase-shifting filter comprises a secondrecursive digital filter having a second phase-versus frequency transferfunction, the second phase-versus-frequency transfer function differingfrom the first phase-versus-frequency transfer function by approximately90 degrees over the predetermined frequency range; wherein said thirdphase-shifting filter comprises a third recursive digital filter havingthe first phase-versus-frequency transfer function; and wherein saidfourth phase-shifting filter comprises a fourth recursive digital filterhaving the second phase-versus-frequency transfer function.